Vectorial Pauli algebraic approach in polarization optics. II. Interaction of light with the canonical polarization devices

Tudor, Tiberiu

doi:10.1016/j.ijleo.2009.08.001

Cited by 10 publications

(4 citation statements)

References 29 publications

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“…Thus, let us look further into Equation (17). It expresses a connection between the Poincaré vectors of the output SOP, s o = p o n o , and of the input SOP, s i = p i n i , in which the characteristic elements of the diattenuator appear mingled.…”

Section: Action Of a Diattenuator On Partially Polarized Light: The C...mentioning

confidence: 99%

“…Its Poincaré axis, n d , appears, its degree of polarization, p d , does not; but, in this respect, we have at hand the basic Equation (9). Evidently, when dealing with dichroic devices, we use full hyperbolic trigonometry and geometry, and, in processing further Equation (17), we have to use the relationships between the hyperbolic functions. We could continue on this inductive way, changing the unexpressive (in this context) hyperbolic parameter η with the degree of dichroism, p d , all the more since cosh η also leads to something expressive:…”

Section: Action Of a Diattenuator On Partially Polarized Light: The C...mentioning

confidence: 99%

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Revisiting Poincaré Sphere and Pauli Algebra in Polarization Optics

Tudor,

Voitcu

2024

Photonics

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We present one of the main lines of development of Poincaré sphere representation in polarization optics, by using largely some of our contributions in the field. We refer to the action of deterministic devices, specifically the diattenuators, on the partial polarized light. On one hand, we emphasize the intimate connection between the Pauli algebraic analysis and the Poincaré ball representation of this interaction. On the other hand, we bring to the foreground the close similarity between the law of composition of the Poincaré vectors of the diattenuator and of polarized light and the law of composition of relativistic admissible velocities. These two kinds of vectors are isomorphic, and they are “imprisoned” in a sphere of finite radius, standardizable at a radius of one, i.e., Poincaré sphere.

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Section: Action Of a Diattenuator On Partially Polarized Light: The C...mentioning

confidence: 99%

Section: Action Of a Diattenuator On Partially Polarized Light: The C...mentioning

confidence: 99%

Revisiting Poincaré Sphere and Pauli Algebra in Polarization Optics

Tudor,

Voitcu

2024

Photonics

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“…It provides at no extra cost an elegant, compact and insightful calculus which highlights the geometric treatment of polarization states. Note that first attempts in this direction root in optics [19]- [23] that provide a clear geometric formulation of Jones formalism. However its generic use for bivariate signal processing is hindered by ignoring phase terms, assuming monochromatism and unpractical implementation.…”

Section: Introductionmentioning

confidence: 99%

A Complete Framework for Linear Filtering of Bivariate Signals

Flamant

Chainais

Bihan

2018

IEEE Trans. Signal Process.

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A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their eigenproperties enabling compact calculus and physically interpretable filtering relations in the frequency domain. The design of filters exhibiting fondamental properties of polarization optics (birefringence, diattenuation) is straightforward. It yields an efficient spectral synthesis method and new insights on Wiener filtering for bivariate signals with prescribed frequency-dependent polarization properties. This generic framework facilitates original descriptions of bivariate signals in two components with specific geometric or statistical properties. Numerical experiments support our theoretical analysis and illustrate the relevance of the approach on synthetic data.

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“…In Section 2 we briefly review some basic results of the vectorial and pure operatorial Pauli algebra's applications in polarization optics (11,12) that will be of use in the present work. In Section 3, starting from the expression of the gain, we show that one can define for the dichroic device a similar quantity as the degree of polarization for the light.…”

Section: Introductionmentioning

confidence: 99%